CAIRO - Hundreds of people chanted anti-U.S. and anti-Islamist slogans outside Hillary Clinton's hotel on Saturday as the U.S. secretary of state urged Egypt's military and Muslim Brotherhood to complete a transition to full democratic rule.

Clinton met Egypt's newly-elected Islamist President Mohamed Mursi on Saturday and was to see military chief Field Marshall Hussein Tantawi on Sunday, two of the central players in the power struggle playing out in the country.

After a more than one-hour meeting with Mursi, Clinton made clear Washington wants Egypt's political players to reach some consensus that would lead to genuine democracy, with the military returning to a purely national security role.

But she stressed it was up to the Egyptians themselves to decide how to achieve this, sorting out such questions as what kind of a constitution to draft and when and whether to hold new parliamentary elections.

"Democracy is hard," Clinton told a news conference with Egyptian Foreign Minister Mohamed Kamel Amr. "It requires dialogue and compromise and real politics."

Clinton got a taste of democracy in action when protesters, most of them backers of the old regime of former President Hosni Mubarak, a long-time U.S. ally toppled by popular protests last year, demonstrated outside her five star hotel.

"Get out Hillary," they chanted. "We don't want the Muslim Brotherhood."